Tubular neighborhoods in the sub-Riemannian Heisenberg groups

Venue:  Seminar Room “-1” – Department of Mathematics
Time: 16:30

• Speaker: Manuel Ritoré (University of Granada)

Abstract:
We consider the Carnot-Carathéodory distance δE to a closed set E in the sub-Riemannian Heisenberg groups ℍn,n≥1.The ℍ-regularity of δE is proved under mild conditions involving a general notion of singular points.
In case E is a Euclidean Ck submanifold, k≥2, we prove that δE is Ck out of the singular set. Explicit expressions for the volume of the tubular neighborhood when the boundary of E is of class C2 are obtained, out of the singular set, in terms of the horizontal principal curvatures of ∂E and of the function ⟨N,T⟩/|Nh| and its tangent derivatives. (https://arxiv.org/abs/1703.01592).

Contact person: Francesco Serra Cassano